Fracture Mechanics 1 : Analysis of Reliability and Quality Control.

Intro -- Title Page -- Contents -- Preface -- Chapter 1. Elements of Analysis of Reliability and Quality Control -- 1.1. Introduction -- 1.1.1. The importance of true physical acceleration life models (accelerated tests = true acceleration or acceleration) -- 1.1.2. Expression for linear acceleration relationships -- 1.2. Fundamental expression of the calculation of reliability -- 1.3. Continuous uniform distribution -- 1.3.1. Distribution function of probabilities (density of probability) -- 1.3.2. Distribution function -- 1.4. Discrete uniform distribution (discrete U) -- 1.5. Triangular distribution -- 1.5.1. Discrete triangular distribution version -- 1.5.2. Continuous triangular law version -- 1.5.3. Links with uniform distribution -- 1.6. Beta distribution -- 1.6.1. Function of probability density -- 1.6.2. Distribution function of cumulative probability -- 1.6.3. Estimation of the parameters (p, q) of the beta distribution -- 1.6.4. Distribution associated with beta distribution -- 1.7. Normal distribution -- 1.7.1. Arithmetic mean -- 1.7.2. Reliability -- 1.7.3. Stabilization and normalization of variance error -- 1.8. Log-normal distribution (Galton) -- 1.9. The Gumbel distribution -- 1.9.1. Random variable according to the Gumbel distribution (CRV, E1 Maximum) -- 1.9.2. Random variable according to the Gumbel distribution (CRV E1 Minimum) -- 1.10. The Frechet distribution (E2 Max) -- 1.11. The Weibull distribution (with three parameters) -- 1.12. The Weibull distribution (with two parameters) -- 1.12.1. Description and common formulae for the Weibull distribution and its derivatives -- 1.12.2. Areas where the extreme value distribution model can be used -- 1.12.3. Risk model -- 1.12.4. Products of damage -- 1.13. The Birnbaum-Saunders distribution -- 1.13.1. Derivation and use of the Birnbaum-Saunders model.

1.14. The Cauchy distribution -- 1.14.1. Probability density function -- 1.14.2. Risk function -- 1.14.3. Cumulative risk function -- 1.14.4. Survival function (reliability) -- 1.14.5. Inverse survival function -- 1.15. Rayleigh distribution -- 1.16. The Rice distribution (from the Rayleigh distribution) -- 1.17. The Tukey-lambda distribution -- 1.18. Student's (t) distribution -- 1.18.1. t-Student's inverse cumulative function law (T) -- 1.19. Chi-square distribution law (χ2) -- 1.19.1. Probability distribution function of chi-square law (χ2) -- 1.19.2. Probability distribution function of chi-square law (χ2) -- 1.20. Exponential distribution -- 1.20.1. Example of applying mechanics to component lifespan -- 1.21. Double exponential distribution (Laplace) -- 1.21.1. Estimation of the parameters -- 1.21.2. Probability density function -- 1.21.3. Cumulated distribution probability function -- 1.22. Bernoulli distribution -- 1.23. Binomial distribution -- 1.24. Polynomial distribution -- 1.25. Geometrical distribution -- 1.25.1. Hypergeometric distribution (the Pascal distribution) versus binomial distribution -- 1.26. Hypergeometric distribution (the Pascal distribution) -- 1.27. Poisson distribution -- 1.28. Gamma distribution -- 1.29. Inverse gamma distribution -- 1.30. Distribution function (inverse gamma distribution probability density) -- 1.31. Erlang distribution (characteristic of gamma distribution, Γ) -- 1.32. Logistic distribution -- 1.33. Log-logistic distribution -- 1.33.1. Mathematical-statistical characteristics of log-logistic distribution -- 1.33.2. Moment properties -- 1.34. Fisher distribution (F-distribution or Fisher-Snedecor) -- 1.35. Analysis of component lifespan (or survival) -- 1.36. Partial conclusion of Chapter 1 -- 1.37. Bibliography.

Chapter 2. Estimates, Testing Adjustments, and Testing the Adequacy of Statistical Distributions -- 2.1. Introduction to assessment and statistical tests -- 2.1.1. Estimation of parameters of a distribution Overview: -- 2.1.2. Estimation by confidence interval -- 2.1.3. Properties of an estimator with and without bias -- 2.2. Method of moments -- 2.3. Method of maximum likelihood -- 2.3.1. Estimation of maximum likelihood -- 2.3.2. Probability equation of reliability-censored data -- 2.3.3. Punctual estimation of exponential law -- 2.3.4. Estimation of the Weibull distribution -- 2.3.5. Punctual estimation of normal distribution -- 2.4. Moving least-squares method -- 2.4.1. General criterion: the LSC -- 2.4.2. Examples of nonlinear models -- 2.4.3. Example of a more complex process -- 2.5. Conformity tests: adjustment and adequacy tests -- 2.5.1. Model of the hypothesis test for adequacy and adjustment -- 2.5.2. Kolmogorov-Smirnov Test (KS 1930 and 1936) -- 2.5.3. Simulated test (1st application) -- 2.5.4. Simulated test (2nd application) -- 2.5.5. Example 1 -- 2.5.6. Example 2 (Weibull or not?) -- 2.5.7. Cramer-Von Mises (CVM) test -- 2.5.8. The Anderson-Darling test -- 2.5.9. Shapiro-Wilk test of normality -- 2.5.10. Adequacy test of chi-square (χ2) -- 2.6. Accelerated testing method -- 2.6.1. Multi-censored tests -- 2.6.2. Example of the exponential model -- 2.6.3. Example of the Weibull model -- 2.6.4. Example for the log-normal model -- 2.6.5. Example of the extreme value distribution model (E-MIN) -- 2.6.6. Example of the study on the Weibull distribution -- 2.6.7. Example of the BOX-COX model -- 2.7. Trend tests -- 2.7.1. A unilateral test -- 2.7.2. The military handbook test (from the US Army) -- 2.7.3. The Laplace test -- 2.7.4. Homogenous Poisson Process (HPP) -- 2.8. Duane model power law.

2.9. Chi-Square test for the correlation quantity -- 2.9.1. Estimations and χ2 test to determine the confidence interval -- 2.9.2. t_test of normal mean -- 2.9.3. Standard error of the estimated difference, s -- 2.10. Chebyshev's inequality -- 2.11. Estimation of parameters -- 2.12. Gaussian distribution: estimation and confidence interval -- 2.12.1. Confidence interval estimation for a Gauss distribution (See appendices) -- 2.12.2. Reading to help the statistical values tabulated -- 2.12.3. Calculations to help the statistical formulae appropriate to normal distribution -- 2.12.4. Estimation of the Gaussian mean of unknown variance -- 2.13. Kaplan-Meier estimator -- 2.13.1. Empirical model using the Kaplan-Meier approach -- 2.13.2. General expression of the KM estimator -- 2.13.3. Application of the ordinary and modified Kaplan-Meier estimator -- 2.14. Case study of an interpolation using the bi-dimensional spline function -- 2.15. Conclusion -- 2.16. Bibliography -- Chapter 3. Modeling Uncertainty -- 3.1. Introduction to errors and uncertainty1 -- 3.2. Definition of uncertainties and errors as in the ISO norm -- 3.3. Definition of errors and uncertainty in metrology -- 3.3.1. Difference between error and uncertainty -- 3.4. Global error and its uncertainty -- 3.5. Definitions of simplified equations of measurement uncertainty -- 3.5.1. Expansion factor k and range of relative uncertainty -- 3.5.2. Determination of type A and B uncertainties according to GUM -- 3.6. Principal of uncertainty calculations of type A and type B -- 3.6.1. Standard and expanded uncertainties -- 3.6.2. Components of type A and type B uncertainties -- 3.6.3. Error on repeated measurements: composed uncertainty -- 3.7. Study of the basics with the help of the GUMic software package: quasi-linear model -- 3.8. Conclusion -- 3.9. Bibliography -- Glossary -- Index.

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